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The use of practically any computing technique itself raises a number of mathematical problems. There is thus a very considerable impact of computation on mathematics itself, and this may be expected to computation on mathematics itself, and this may be expected to influence mathematical research to an increasing degree.

[Computers] are developing so rapidly that even computer scientists cannot keep up with them. It must be bewildering to most mathematicians and engineers... In spite of the diversity of the applications, the methods of attacking the difficult problems with computers show a great unity, and the name of Computer Sciences is being attached to the discipline as it emerges. It must be understood, however, that this is still a young field whose structure is still nebulous. The student will find a great many more problems than answers.

Forsythe (1961) "Engineering students must learn both computing and mathematics". J. Eng. Educ. 52 (1961), p. 177. as cited in (Knuth, 1972) According to Donald Knuth in this quote Forsythe coined the term "computer science".

To a modern mathematician design seems to be a second rate intellectual activity

Machine-held strings of binary digits can simulate a great many kinds of things, of which numbers are just one kind. For example, they can simulate automobiles on a freeway, chess pieces, electrons in a box, musical notes, Russian words, patterns on a paper, human cells, colors, electrical circuits, and so on. To think of a computer as made up essentially of numbers is simply a carryover from the successful use of mathematical analysis in studying models. Most of this series of lectures has been devoted to applications of computers, and this is not the time to give details about their usefulness. I merely wish to point out certain types of things being done with computers today that could not have been done in 1945. Some of these are technological, some are intellectual.

Whether computers are used for engineering design, medical data processing, composing music, or other purposes, the structure of computing is much the same. We are extremely short of talented people in this field, and so we need departments, curricula, and research and degree programs in computer science... I think of the Computer Science Department as eventually including experts in Programming, Numerical Analysis, Automata Theory, Data Processing, Business Games, Adaptive Systems, Information Theory, Information Retrieval, Recursive Function Theory, Computer Linguistics, etc., as these fields emerge in structure... Universities must respond [to the computer revolution] with far reaching changes in the educational structure.

George Forsythe, in a recent paper “A University's Educational Program in Computer Science,” points out that the ordinary computer is one of the most important tools devised in the history of man, the third giant step in man's intellectual history.

The only generally agreed upon definition of mathematics is "Mathematics is what mathematician's do."… In the face of this difficulty [of defining "computer science"] many people, including myself at times, feel that we should ignore the discussion and get on with doing it. But as George Forsythe points out so well in a recent article*, it does matter what people in Washington D.C. think computer science is. According to him, they tend to feel that it is a part of applied mathematics and therefore turn to the mathematicians for advice in the granting of funds. And it is not greatly different elsewhere; in both industry and the universities you can often still see traces of where computing first started, whether in electrical engineering, physics, mathematics, or even business. Evidently the picture which people have of a subject can significantly affect its subsequent development. Therefore, although we cannot hope to settle the question definitively, we need frequently to examine and to air our views on what our subject is and should become.